Structured covariance matrices characterized by a small number of parameters have been widely used and play an important role in parameter estimation and statistical inference. To assess the adequacy of a specified covariance structure, one often adopts the classical likelihood-ratio test when the dimension of the data (p) is smaller than the sample size (n). However, this assessment becomes quite challenging when p is bigger than n, since the classical likelihood-ratio test is no longer applicable. In this talk, an adjusted goodness-of-fit test will be introduced to examine a broad range of covariance structures under the scenario of “large p, small n”. Some analytical examples and large sample properties will be presented to illustrate the effectiveness of adjustment for assessing the goodness-of-fit of covariance. In addition, numerical examples and a real data application will be provided to demonstrate the performance and the practical utility of the proposed method.
More information about Ping-Shou Zhong may be found at http://www.stt.msu.edu/People/people.aspx?member=pszhong